// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Vincent Lejeune
// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_BLOCK_HOUSEHOLDER_H
#define EIGEN_BLOCK_HOUSEHOLDER_H

// This file contains some helper function to deal with block householder reflectors

namespace Eigen {

namespace internal {

    /** \internal */
    // template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
    // void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
    // {
    //   typedef typename VectorsType::Scalar Scalar;
    //   const Index nbVecs = vectors.cols();
    //   eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
    //
    //   for(Index i = 0; i < nbVecs; i++)
    //   {
    //     Index rs = vectors.rows() - i;
    //     // Warning, note that hCoeffs may alias with vectors.
    //     // It is then necessary to copy it before modifying vectors(i,i).
    //     typename CoeffsType::Scalar h = hCoeffs(i);
    //     // This hack permits to pass trough nested Block<> and Transpose<> expressions.
    //     Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);
    //     Scalar Vii = *Vii_ptr;
    //     *Vii_ptr = Scalar(1);
    //     triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()
    //                                        * vectors.col(i).tail(rs);
    //     *Vii_ptr = Vii;
    //     // FIXME add .noalias() once the triangular product can work inplace
    //     triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
    //                              * triFactor.col(i).head(i);
    //     triFactor(i,i) = hCoeffs(i);
    //   }
    // }

    /** \internal */
    // This variant avoid modifications in vectors
    template <typename TriangularFactorType, typename VectorsType, typename CoeffsType>
    void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
    {
        const Index nbVecs = vectors.cols();
        eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows() >= nbVecs);

        for (Index i = nbVecs - 1; i >= 0; --i)
        {
            Index rs = vectors.rows() - i - 1;
            Index rt = nbVecs - i - 1;

            if (rt > 0)
            {
                triFactor.row(i).tail(rt).noalias() =
                    -hCoeffs(i) * vectors.col(i).tail(rs).adjoint() * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();

                // FIXME use the following line with .noalias() once the triangular product can work inplace
                // triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();
                for (Index j = nbVecs - 1; j > i; --j)
                {
                    typename TriangularFactorType::Scalar z = triFactor(i, j);
                    triFactor(i, j) = z * triFactor(j, j);
                    if (nbVecs - j - 1 > 0)
                        triFactor.row(i).tail(nbVecs - j - 1) += z * triFactor.row(j).tail(nbVecs - j - 1);
                }
            }
            triFactor(i, i) = hCoeffs(i);
        }
    }

    /** \internal
  * if forward then perform   mat = H0 * H1 * H2 * mat
  * otherwise perform         mat = H2 * H1 * H0 * mat
  */
    template <typename MatrixType, typename VectorsType, typename CoeffsType>
    void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward)
    {
        enum
        {
            TFactorSize = MatrixType::ColsAtCompileTime
        };
        Index nbVecs = vectors.cols();
        Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs, nbVecs);

        if (forward)
            make_block_householder_triangular_factor(T, vectors, hCoeffs);
        else
            make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());
        const TriangularView<const VectorsType, UnitLower> V(vectors);

        // A -= V T V^* A
        Matrix<typename MatrixType::Scalar,
               VectorsType::ColsAtCompileTime,
               MatrixType::ColsAtCompileTime,
               (VectorsType::MaxColsAtCompileTime == 1 && MatrixType::MaxColsAtCompileTime != 1) ? RowMajor : ColMajor,
               VectorsType::MaxColsAtCompileTime,
               MatrixType::MaxColsAtCompileTime>
            tmp = V.adjoint() * mat;
        // FIXME add .noalias() once the triangular product can work inplace
        if (forward)
            tmp = T.template triangularView<Upper>() * tmp;
        else
            tmp = T.template triangularView<Upper>().adjoint() * tmp;
        mat.noalias() -= V * tmp;
    }

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_BLOCK_HOUSEHOLDER_H
